Shoaib Muhammad, Shah Farooq Ahmed, Nisar Kottakkaran Sooppy, Raja Muhammad Asif Zahoor, Haq Ehsan Ul, Abbasi Aqsa Zafar, Hassan Qazi Mahmood Ul, Al-Harbi Nuha, Abdel-Aty Abdel-Haleem
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan.
Yuan Ze University, AI Center, Taoyuan 320, Taiwan.
Heliyon. 2023 Mar 9;9(3):e14365. doi: 10.1016/j.heliyon.2023.e14365. eCollection 2023 Mar.
This article aims to investigate the analytical nature and approximate solution of the radiated flow of electrically conductive viscous fluid into a porous medium with slip effects (RFECVF). In order to build acceptable accurate solutions for RFECVF, this study presented an efficient Levenberg-Marquardt technique of artificial neural networks (LMT-ANNs) approach. One of its fastest back-propagation algorithms for nonlinear lowest latency is the LMT. To turn a quasi-network of PDEs expressing RFECVF into a set of standards, the appropriate adjustments are required. During the flow, the boundary is assumed to be convective. The flow and heat transfer are governed by partial differential equations, and similarity transform is the main tool to convert it into a coupled nonlinear system of ODEs. The usefulness of the constructed LMT-ANNs for such a modelled issue is demonstrated by the best promising algebraic outputs in the E-03 to E-08 range, as well as error histogram and regression analysis measures. Mu is a controller that oversees the entire training procedure. The LMT-ANNs mainly focuses on the higher accuracy of nonlinear systems. Analytical results for the improved boundary layer ODEs are produced using the Variational Iteration Method, a tried-and-true method (VIM). The Lagrange Multiplier is a powerful tool in the suggested method for reducing the amount of computing required. Further, a tabular comparison is provided to demonstrate the usefulness of this study. The final results of the Variational Iteration Method (VIM) in MATLAB have accurately depicted the physical characteristics of a number of parameters, including Eckert, Prandtl, Magnetic, and Thermal radiation parameters.
本文旨在研究具有滑移效应的导电粘性流体向多孔介质的辐射流动（RFECVF）的解析性质和近似解。为了构建适用于RFECVF的准确解，本研究提出了一种高效的人工神经网络Levenberg-Marquardt技术（LMT-ANNs）方法。LMT是其用于非线性最低延迟的最快反向传播算法之一。为了将表示RFECVF的偏微分方程准网络转化为一组标准，需要进行适当的调整。在流动过程中，假设边界为对流边界。流动和传热由偏微分方程控制，相似变换是将其转化为耦合非线性常微分方程组的主要工具。在E-03至E-08范围内最有前景的代数输出以及误差直方图和回归分析测量结果证明了所构建的LMT-ANNs对于此类建模问题的有效性。Mu是一个监督整个训练过程的控制器。LMT-ANNs主要关注非线性系统的更高精度。使用变分迭代法（VIM）这一经过验证的方法得出了改进边界层常微分方程的解析结果。拉格朗日乘数是所提出方法中减少所需计算量的有力工具。此外，还提供了表格比较以证明本研究的有效性。变分迭代法（VIM）在MATLAB中的最终结果准确地描述了包括埃克特、普朗特、磁和热辐射参数在内的多个参数的物理特性。
